Boundary conditions applied on bearing corner in direct aluminum extrusion

Finite element analysis in aluminum extrusion is faced by several problems such as number of degrees of freedom, calculation time, large deformation and flow conservation. The problem of large deformation is overcome by applying the Eulerian formulation. But the problems concerning number of degrees of freedom, calculation time can be overcome by the model simplification especially at the bearing corner. On the one hand, detailed modeling of the bearing corner will increase the complexity of the analysis. On the other hand, simplified modeling of the bearing corner will face problems such as locking of the corner node and flow conservation. Therefore, boundary conditions will be applied at the corner node in order to solve the problem of its locking and to satisfy the aluminum flow conservation. These boundary conditions include normal and constraint equation. This paper focuses on the calculation of the normal with different elements such as plane strain, axisymmetric and tetrahedron elements. The constraint equation at different positions of the corner node is determined for a plane strain element only. The extrusion force and average exit velocity are investigated and compared with the triple node method and reference model. Where, in the reference model the contact boundary condition is applied between the rigid die and aluminum. Eulerian formulation is applied in finite element analysis unless in the reference model the Arbitrary Lagrangian Eulerian formulation is applied

3-D Numerical Simulation of Direct Aluminum Extrusion and Die Deformation

The design of extrusion dies depends on the experience of the designer. After the die has been manufactured, it is tested during an extrusion process and machined several times until it works properly. Therefore, the die is designed by a trial and error method which is an expensive process. In addition, after several runs the die may deform. This may lead to an unacceptable product. This paper focuses on 3-D simulation of a direct aluminum extrusion process. The behavior of the billet and die is predicted. In the simulation an Eulerian formulation is applied to simulate the flow of the material, rather than an Updated Lagragian formulation with remeshing. Finally, the results will illustrate how the die deforms and whether it deforms elastically or plastically and the influence of die deformation on the extruded product dimensions

Exact diagonalization study of the tunable edge magnetism in graphene

The tunable magnetism at graphene edges with lengths of up to 48 unit cells is analyzed by an exact diagonalization technique. For this we use a generalized interacting one-dimensional model which can be tuned continuously from a limit describing graphene zigzag edge states with a ferromagnetic phase, to a limit equivalent to a Hubbard chain, which does not allow ferromagnetism. This analysis sheds light onto the question why the edge states have a ferromagnetic ground state, while a usual one-dimensional metal does not. Essentially we find that there are two important features of edge states: (a) umklapp processes are completely forbidden for edge states; this allows a spin-polarized ground state. (b) the strong momentum dependence of the effective interaction vertex for edge states gives rise to a regime of partial spin-polarization and a second order phase transition between a standard paramagnetic Luttinger liquid and ferromagnetic Luttinger liquid.Comment: 11 pages, 8 figure

Doping induced metal-insulator transition in two-dimensional Hubbard, t−Ut-U, and extended Hubbard, t−U−Wt-U-W, models

We show numerically that the nature of the doping induced metal-insulator transition in the two-dimensional Hubbard model is radically altered by the inclusion of a term, $W$, which depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length, $\xi_l$, in the insulating state. At finite values of $W$ we find results consistent with $\xi_l \sim | \mu - \mu_c|^{- 1/2}$ where $\mu_c$ is the critical chemical potential. In contrast, $\xi_l \sim | \mu - \mu_c|^{-1/4}$ for the Hubbard model. At finite values of $W$, the presented numerical results imply that doping the antiferromagnetic Mott insulator leads to a $d_{x^2 - y ^2}$ superconductor.Comment: 19 pages (latex) including 7 figures in encapsulated postscript format. Submitted for publication in Phys. Rev.

Charge and Spin Structures of a dx2−y2d_{x^2 - y^2} Superconductor in the Proximity of an Antiferromagnetic Mott Insulator

To the Hubbard model on a square lattice we add an interaction, $W$, which depends upon the square of a near-neighbor hopping. We use zero temperature quantum Monte Carlo simulations on lattice sizes up to $16 \times 16$, to show that at half-filling and constant value of the Hubbard repulsion, the interaction $W$ triggers a quantum transition between an antiferromagnetic Mott insulator and a $d_{x^2 -y^2}$ superconductor. With a combination of finite temperature quantum Monte Carlo simulations and the Maximum Entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite temperature Kosterlitz-Thouless transition to the $d_{x^2 -y^2}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature, $T_{KT}$, we compute the one-electron density of states, $N(\omega)$, the spin relaxation rate $1/T_1$, as well as the imaginary and real part of the spin susceptibility $\chi(\vec{q},\omega)$. The spin dynamics are characterized by the vanishing of $1/T_1$ and divergence of $Re \chi(\vec{q} = (\pi,\pi), \omega = 0)$ in the low temperature limit. As $T_{KT}$ is approached $N(\omega)$ develops a pseudo-gap feature and below $T_{KT}$ $Im \chi(\vec{q} = (\pi,\pi), \omega)$ shows a peak at finite frequency.Comment: 46 pages (latex) including 14 figures in encapsulated postscript format. Submitted for publication in Phys. Rev.

Critical Exponents of the Metal-Insulator Transition in the Two-Dimensional Hubbard Model

We study the filling-controlled metal-insulator transition in the two-dimensional Hubbard model near half-filling with the use of zero temperature quantum Monte Carlo methods. In the metallic phase, the compressibility behaves as $\kappa \propto |\mu - \mu_c|^{-0.58\pm0.08}$ where $\mu_c$ is the critical chemical potential. In the insulating phase, the localization length follows $\xi_l \propto |\mu - \mu_c|^{-\nu_l}$ with $\nu_l = 0.26 \pm 0.05$. Under the assumption of hyperscaling, the compressibility data leads to a correlation length exponent $\nu_\kappa = 0.21 \pm 0.04$. Our results show that the exponents $\nu_\kappa$ and $\nu_l$ agree within statistical uncertainty. This confirms the assumption of hyperscaling with correlation length exponent $\nu = 1/4$ and dynamical exponent $z = 4$. In contrast the metal-insulator transition in the generic band insulators in all dimensions as well as in the one-dimensional Hubbard model satisfy the hyperscaling assumption with exponents $\nu = 1/2$ and $z = 2$.Comment: Two references added. The DVI file and PS figure files are also available at http://www.issp.u-tokyo.ac.jp/labs/riron/imada/furukawa/; to appear in J. Phys. Soc. Jpn 65 (1996) No.

Dynamic Exponent of t-J and t-J-W Model

Drude weight of optical conductivity is calculated at zero temperature by exact diagonalization for the two-dimensional t-J model with the two-particle term, $W$. For the ordinary t-J model with $W$=0, the scaling of the Drude weight $D \propto \delta^2$ for small doping concentration $\delta$ is obtained, which indicates anomalous dynamic exponent $z$=4 of the Mott transition. When $W$ is switched on, the dynamic exponent recovers its conventional value $z$=2. This corresponds to an incoherent-to-coherent transition associated with the switching of the two-particle transfer.Comment: LaTeX, JPSJ-style, 4 pages, 5 eps files, to appear in J. Phys. Soc. Jpn. vol.67, No.6 (1998

Understanding the Josephson current through a Kondo-correlated quantum dot

We study the Josephson current 0-$\pi$ transition of a quantum dot tuned to the Kondo regime. The physics can be quantitatively captured by the numerically exact continuous time quantum Monte Carlo method applied to the single-impurity Anderson model with BCS superconducting leads. For a comparison to an experiment the tunnel couplings are determined by fitting the normal-state linear conductance. Excellent agreement for the dependence of the critical Josephson current on the level energy is achieved. For increased tunnel couplings the Kondo scale becomes comparable to the superconducting gap and the regime of the strongest competition between superconductivity and Kondo correlations is reached; we predict the gate voltage dependence of the critical current in this regime.Comment: 5 pages, 3 figure